Hope you don't mind my jumping in here and giving you some resources to help you narrow things down. First is when going to Ireland people expect to find things in a day or two and not leaving enough time. Generally what happens you end up being a frustrated tourist and having to go back again once you have your duckies in order.
These websites will help you narrow things down a bit.
Fermagh is particularily difficult as most online website do not have early records. I haven't been able to find a complete answer but one thing I do know is the government at one time collected all parish records and these were destroyed by fire in 1922. The existing ones were copied by priests from the originals so they basically had the information. It is only coming on line bit by bit. A good website for Fermanagh parish records, tithe's 1824 and other excellent information:www.censusfinder.com
has many records on the main website, including the 1880 USA,UK and CA census. If nothing there try the new PILOT PROGRAM, they put online 2/09 it was just recently updated again. This is found top left corner of main website under 'search records' drop down menu and click on PILOT. There are US census and passenger records
as well as bmd's. The very early birth years were determined by death's in Ireland and age of the person at the time.
Andrew McCullough died July-Sept,1908,73 born abt1835. Irvinestown Registration District, Co.Fermanagh/Tyrone.www.failteromhat.com
(land descriptions) has the Griffiths Valuation of the 1860's a bit late perhaps but it certainly shows the Parishes and Townland.
eg: McCullough's in 1862 when the valuations were done. Only 16 in all, 12 of Devenish Parish and various townlands, 1 Aghalurcher Parish, 1 Drumkeeran Parish. www.from-ireland.net
explains the different divisions for Ireland. County, Diocese, Parish and Townlands, Poor Law Union, Civil Registration etc.
Try googling churches in the area and find through tourist sites and googles maps. Most Diocese are on line and also local churches some with email addresses. RC records can be accessed by contacting the clergy and making an appointment to see them when in Ireland, some cooperate and some don't.
Church of Ireland records are kept in Dublin at the Representative Library, a short distance 30 min by bus for records prior to 1899. They are online also so you should email and see if they have the records for Fermanagh as I'm not sure if this Library has Northern Ireland records. The National Library in Dublin has records as will PRONI in Belfast both on line.
If I think of anything else I will get back to you.
'genealogy for fun'